A narrowband active noise control system with autoregressive model and linear cascaded adaptive notch filter
Introduction
Noise pollution brings serious effects to human life financially, spiritually, especially in production activity. The traditional passive noise canceling method performs poorly in low frequency while active noise control (ANC) shows dramatically excellent noise reduction properties so that it has been widely investigated [1]. In the case of narrowband ANC (NANC) system with typical filtered-X LMS (FXLMS) algorithm [2], [3], a non-acoustic sensor is usually used while it suffers from a crucially fatal problem-frequency mismatch (FM)-for the abrasion and aging of the sensor after long-term use as well as the inability of processing with unstable noise, which leads to the degradation of the performance of the NANC system even contributes to invalidation [4].
Many works have been analytically revealed the FM effects on the NANC system [5], [6], [7], [8], [9], [10]. For the nature of NANC system, the most common way to eliminate the influence caused by FM is to improve the accuracy of the reference signals fed to the system, namely, improving the accuracy of reference frequencies being tracked, estimated, or regulated. The typical frequency tracking method is adopting autoregressive (AR) model, which can adaptively track the reference frequency and generate reference signal for the NANC system, but it still needs a non-acoustic sensor to get a synchronization signal (e.g., rotating speed) and then calculate the original value for its coefficient [4], [6], [11], [12], [13]. The widely-used method for frequency estimation is adopting the 2nd order infinite impulse response (IIR) adaptive notch filter (ANF) [14], [15], [16]. An ANF estimates one frequency, so cascaded ANF, such as linear cascaded ANF (LCANF) and triangular cascaded ANF (TCANF), can be used to estimate multiple components [17]. However, there still exists a little difference between the frequencies estimated by LCANF and the real frequencies, which also leads to FM. And as for the TCANF, although it tracks frequencies accurately, it suffers from the high computational load for the complicated additional ANFs. To solve this problem, in [18], a parallel ANF (PANF) algorithm to obtain more accurate frequency estimation without increasing computational complexity was proposed. However, the system fluctuates when the frequency estimation is affected by random noise even though the influence is tiny. This relatively small FM shows that even if the reference frequencies are estimated well in appearance, the narrowband noise can not be effectively suppressed. And with FM increasing, the control performance declines. In [19], a simplified system with a frequency estimator based on Bayesian inference combined with ANFs was proposed, which can obtain accurate frequencies as well as the number of frequency components. And other novel reference frequency regulators or estimators based on minimum variance distortion-less response (MVDR) iteration algorithm, weighted-frequency way, and adaptive line enhancer (ALE) have been recently proposed for accommodating FM [20], [21], [22], [23], but they suffer from high computation complexity especially when dealing with multiple frequencies, or even are merely applicable when dealing with fundamental and harmonic frequencies.
As for the adaptive algorithm for the iteration of IIR type ANF, a plain gradient (PG) algorithm which has fast convergence and low-cost computation was proposed in [24]. But it still suffers from the weakness of a little gap between the estimated frequencies and the real ones. In [25], an average indirect plain gradient (AIPG) based indirect frequency estimation algorithm was proposed. It is supposed to solve the problems of slow convergence, unstable error, and limited selection of iterative initial values of the existing ANF-based frequency estimation methods. This algorithm improves little additional computation while is unable to deal with multiple frequencies, which may be caused by the interaction between the different frequencies.
This paper estimates frequency with a simplified LCANF in indirect form, based on the PG algorithm, which has a relatively smaller computation load compared with the one based on the Burg algorithm [18], [19], [26]. In order to acquire more accurate estimation results and track frequency-varying signals, the AR model is adopted. The LCANF algorithm estimates the approximate frequencies with provided zero initial values, and the AR model provides a higher frequency tracking accuracy. Based on the proposed structure above, the NANC system only needs the error microphone instead of an additional non-acoustic sensor to get the synchronization signal and has a good performance in convergence speed and the excellent noise reduction ability.
The remainder of this paper is constructed as follows. The proposed NANC system based on the LCANF algorithm combined with the AR model is described in detail in Section 2. Section 3 conducts representative simulations to demonstrate the performance of the proposed system in accommodating FM. Conclusions are given in Section 4.
Section snippets
A NANC system with the LCANF and the AR model
The block diagram of the designed NANC system with the LCANF and the AR model is illustrated in Fig. 1. In this context, the primary noise signal is expressed aswhere, is the number of frequency components contained in the primary noise, is the th component noise signal with amplitude and frequency , is usually assumed as an additive white Gaussian noise with mean of 0 and variance , and is the sampling frequency. An unit
Simulations
In this section, representative simulations are conducted to demonstrate the performance of the proposed NANC system with the LCANF algorithm combined with the AR model. In all the simulations, the sampling frequency is 2.5 kHz, the additive white Gaussian noise is set with mean of 0 and variance of 0.01. Besides, in the simulation results, the real noise frequency is denoted as .
Conclusions
A NANC system based on the LCANF with the PG algorithm combined with the AR model is proposed in this paper. Despite initial settings of the frequencies, this system works well as well as has a low computational load and simple structure. The frequency estimators offer approximate initial-estimated frequencies with a fast speed, then the NANC system with the AR model tracks the frequencies adaptively with fast convergence and reaches an excellent noise reduction performance. Because of the
CRediT authorship contribution statement
Jian Liu: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – review & editing, Visualization, Supervision, Project administration, Funding acquisition. Zhixin Wang: Software, Writing – original draft, Validation, Formal analysis, Investigation, Data curation, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported in part by the Fundamental Research Funds for the Central Universities (NO. NJ2020014). The authors would like to thank the Handling Editor Prof. Balu Santhanam and anonymous reviewers for providing rich and instructive feedback and suggestions to improve the quality and presentation of the paper.
References (28)
- et al.
An exact analysis of the lms algorithm with tonal reference signals in the presence of frequency mismatch
Signal process.
(2005) - et al.
Analysis and compensation of reference frequency mismatch in multiple-frequency feedforward active noise and vibration control system
J. Sound Vib.
(2017) - et al.
Improving active control of fan noise with automatic spectral reshaping for reference signal
Appl. Acoust.
(2015) - et al.
On-line fundamental frequency tracking method for harmonic signal and application to anc
J. Sound Vib.
(2001) - et al.
A narrowband active noise control system with a frequency estimation algorithm based on parallel adaptive notch filter
Signal process.
(2019) - et al.
A narrowband active noise control system with a frequency estimator based on bayesian inference
J. Sound Vib.
(2019) - et al.
A new robust frequency mismatch removing approach with variable step-size algorithm
Proc. ICSV 25
(2018) - et al.
Active Noise Control Systems: Algorithms and DSP Implementations
(1996) An analysis of multiple correlation cancellation loops with a filter in the auxiliary path
IEEE Trans. Acoust., Speech, Signal Process.
(1980)Active adaptive sound control in a duct: a computer simulation
J. Acoust. Soc. Am.
(1981)
A robust narrowband active noise control system for accommodating frequency mismatch
Proc. Eur. Signal Process. Conf.
A new robust narrowband active noise control system in the presence of frequency mismatch
IEEE Trans. Audio, Speech, Lang. Process.
Analysis and correction of frequency error in electronic mufflers using narrowband active noise control
Proc. IEEE Int. Conf. Contr. Appl.
A filtered-x lms algorithm for sinusoidal reference signals-effects of frequency mismatch
IEEE Signal Process. Lett.
Cited by (6)
A narrowband active noise control system with coarse frequency estimator and spectrum shifter
2023, Mechanical Systems and Signal ProcessingStatistical analysis of multichannel FxLMS algorithm for narrowband active noise control
2022, Signal ProcessingCitation Excerpt :Narrowband noise is the noise generated by rotating machinery such as propellers [1–5], and is also known as tonal, periodic, or harmonic noise. The narrowband active noise control (NANC) system is a control system that suppresses narrowband noise [6–10]. Owing to its excellent performance, the NANC system is widely used to control fan noise and engine noise [11–15].
Multi-reference Adaptive Gain FXLMS Algorithm for Active Noise Control
2023, 2023 8th International Conference on Computer and Communication Systems, ICCCS 2023Research on Narrowband Active Noise Control in the Hydraulic Excavator Cabin
2022, Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University